The theory of classical statistics assumes crisp, certain, and clear observations/parameters in engineering applications. However, in such engineering applications, due to their complex functions, it ...may not possible to obtain clear or crisp values of certain parameters. So, there is a chance of obtaining indeterminate, imprecise, vague, and incomplete parameters. In this situation, neutrosophic statistics can be applied, which is the generalization of classical statistics. This is reduced to classical statistics when no parameters are found to be indeterminate, imprecise, vague, or incomplete in actual practice. In this paper, we design a new sampling plan using the neutrosophic approach for the process loss function. The neutrosophic non-linear problem is given and applied to determine the neutrosophic plan parameters of the proposed sampling plan. A table is given and discussed with the help of factory data.
The time truncated plan for the Weibull distribution under the indeterminacy is presented. The plan parameters of the proposed plan are determined by fixing the indeterminacy parameter. The plan ...parameters are given for various values of indeterminacy parameters. From the results, it can be concluded that the values of sample size reduce as indeterminacy values increase. The application of the proposed plan is given using wind speed data. From the wind speed example, it is concluded that the proposed plan is helpful to test the average wind speed at smaller values of sample size as compared to existing sampling plan.
The existing analysis of variance (ANOVA) test cannot be applied when the sample is selected from the population having come imprecise, fuzzy and uncertain observations. The neutrosophic statistics ...will be applied to analyze the data having uncertain observations or the parameters. In this paper, we will introduce the neutrosophic analysis of variance (NANONA). The NANONA is an extension of the classical ANOVA. We presented the NANONA table. We performed the NANONA to test teaching methods using data collected from the university students.
In the present paper, two important measures of skewness and kurtosis under indeterminacy are presented. The basic measures to evaluate the nature of the wind speed in the presence of neutrosophic ...numbers are given. The importance of the proposed measures of skewness and kurtosis under neutrosophic statistics is discussed over the existing measures of skewness and kurtosis under classical statistics. From the wind speed analysis, it is concluded that the wind speed data have heavy-tailed distribution. Therefore, it is recommended to apply a heavy-tailed distribution, like Cauchy distribution, for forecasting and estimation of energy produced by wind speed.
The existing F-test for two counts data from the Poisson distribution under classical statistics can be applied only when the counts in the data are exact or not intervals. The existing test cannot ...be applied when the count data is indeterminate, in the interval, and uncertain. In this paper, the F-test for two counts data from the Poisson distribution under classical statistics is designed. The test for two counts recording at the same time or different times is presented. The daily and the monthly number of records broken data in the U.S from the weather department is selected for the application of the proposed test. The application and comparison studies show the efficiency of the proposed test. The proposed test was found to be informative, flexible, and appropriate to be applied in an uncertain environment.
Abstract
Background
The data obtained from the counting process is known as the count data. In practice, the counting can be done at the same time or the time of the count is not the same. To test ...either the K counts are differed significantly or not, the Chi-square test for K counts is applied.
Results
The paper presents the Chi-square tests for K counts under neutrosophic statistics. The test statistic of the proposed test when K counts are recorded at the same time and different time are proposed. The testing procedure of the proposed test is explained with the help of pulse count data.
Conclusions
From the analysis of pulse count data, it can be concluded that the proposed test suggests the cardiologists use different treatment methods on patients. In addition, the proposed test gives more information than the traditional test under uncertainty.
The existing Z-test for uncertainty events does not give information about the measure of indeterminacy/uncertainty associated with the test.
This paper introduces the Z-test for uncertainty events ...under neutrosophic statistics. The test statistic of the existing test is modified under the philosophy of the Neutrosophy. The testing process is introduced and applied to the Covid-19 data.
Based on the information, the proposed test is interpreted as the probability that there is no reduction in uncertainty of Covid-19 is accepted with a probability of 0.95, committing a type-I error is 0.05 with the measure of an indeterminacy 0.10. Based on the analysis, it is concluded that the proposed test is informative than the existing test. The proposed test is also better than the Z-test for uncertainty under fuzzy-logic as the test using fuzz-logic gives the value of the statistic from 2.20 to 2.42 without any information about the measure of indeterminacy. The test under interval statistic only considers the values within the interval rather than the crisp value.
From the Covid-19 data analysis, it is found that the proposed Z-test for uncertainty events under the neutrosophic statistics is efficient than the existing tests under classical statistics, fuzzy approach, and interval statistics in terms of information, flexibility, power of the test, and adequacy.
The sampling plan using the classical statistics under the exponential distribution can be applied only when there are certainty and clearness and in observations and parameters. But, in practice, it ...is not necessary that under some circumstances all the observations/parameters are determined. So, we cannot analyze them using the classical statistics which provides results in the determined values. The neutrosophic statistics which is the generation of classical statistics can be applied to the analysis when parameters/observations are incomplete, indeterminate, and vague imprecise. In this paper, we will design originally a sampling plan for the exponential distribution under the neutrosophic interval statistical method. The neutrosophic plan parameters of the proposed plan will be determined through the neutrosophic non-linear problem. The tables for various values of risk are presented for the use in the industrial. An example from the automobiles manufacturing industry is given to explain for the exponential distribution under the neutrosophic interval statistical method.
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